**Curriculum**

**Curriculum**

### Math

#### ★ Venn Diagrams

U is the universal set

“elements” are inside a set

∩ = intersection (the overlap)

∪ = union (everything together)

The “complement” of a set is everything outside (noted with a ‘ )

#### ★ Set Notation

*Number Sets*

*R* = Real

*Z* = Integers (*Z⁺ *= positive integers, *Z⁻* = negative integers)

*N* = Natural

*Q* = Rational

*I* = Irrational

⊂ = Subset (⊆ a subset which can be equal to original set)

Example: *N* ⊂ *Z* ⊂ *R*

∈ = “element of”

∉ = “not an element of”

Examples: 2 ∈ *Z⁺*, but 2 ∉ *Z⁻*

Example: U = { x | x<10, x ∈ *N* }, A = {1, 3, 6, 8}, A’ = {2, 4, 5, 7, 9}

This reads as “The Universal Set is the set of all values such that the value is less than 10 as well as a Natural Number. If the Set A contains 1, 3, 6, and 8, then the Complement of Set A must contain 2, 4, 5, 7, and 9.”

Laws of Algebra of Sets (p.37 in text)

#### ★ Factoring

“Un-distributing”

“Un-FOIL”

#### ★ Simplifying

Numbers and variables in a fraction

Rational expressions

Factor and simplify

#### ★ Evaluating Expressions

Variables are defined, and then expression is evaluated

#### ★ Simplifying Rational Expressions

**Addition** — Common denominators are needed

**Subtraction** — Common denominators are needed. Remember that *everything after* the subtraction sign has the sign changed

**Multiplication** — Just multiply straight across and simplify

**Division** — “Keep, Change, Flip”, then multiply straight across and simplify

★ Writing Formula

★ Laws of Exponents

Multiplying with the same base – add the exponents

Dividing with the same base – subtract the exponents

Simplest Radical Form (never a radical in the denominator)

★ Rationalizing the Denominator

√ can not be in the denom’ – multiply by denom/denom (which is the same as just multiplying by 1)

If a+b√ is in the denom, then multiply by a-b√ (then the √ term will cancel)

If there are two √ in the fraction, then rationalize twice

★ System of Equations (aka “Simultaneous Equations”)

1 variable, 1 equation… 2 variables, 2 equations are needed

Setting up systems which match the form a+b√

Solve by the process of elimination, then check

★ Trigonometry

Pythagorean Theorem: a² + b² = c²

(where c is always the hypotenuse of the right triangle)

Trig’ Functions (sine, cosine, tangent)

SOH CAH TOA

O=Opposite, A=Adjacent, H=Hypotenuse

Identify which 2 sides, then use corresponding trig’ function

Inverse Trig’ Functions (used to find missing angles)

Breaks apart the trig’ function from the x

★ Bearings

True bearings are always from North, clockwise

Make parallel lines to make a “Z” to see congruent angles

★ Law of Sines

a/SinA = b/SinB = c/SinC

Use when you have 2 angles

★ Law of Cosines

a² = b² + c² – 2bc•CosA

b² = a² + c² – 2ac•CosB

c² = a² + b² – 2ab•CosC

Use when you have 3 sides

CosA = (b² + c² – a²) / 2bc

This is the same as above, just rearranged

Use when you have 3 sides and need to find the angle

★ Analyzing Data

Dot Plots

Column Graphs

The x-axis is always the independent variable (usually time, or something else that is not dependent on anything)

### Biology

– Review of cells and tissues.

– Characteristics of living organisms.

– Vocabulary review of the characteristics of living organisms.

– Viruses and examples of living organisms.

– Classification of living organisms.

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**Materials & Links**

**Materials & Links**

*Our Meetings*

*Our Meetings*

✓ Aug 31, Thurs – Math (18:30-20:30) – 2 hrs

✓ Sept 05, Tues – Math (18:30-20:30) – 2 hrs

~~☐ Sept 12 – (skipped for class trip)~~

✓ Sept 19, Tues – Math (18:30-20:30) – 2 hrs

✓ Sept 25, Wed – Math (18:30-20:30) – 2 hrs

✓ Oct 03, Tues – Math (17:00-18:30) – 1.5 hrs

✓ Oct 05, Thurs – Math (19:35-21:05) – 1.5 hrs

✓ Oct 10, Tues – Math (18:30-20:00) – 1.5 hrs

✓ Oct 11, Wed – Bio (18:30-19:30) – 1 hr

✓ Oct 12, Thurs – Math (17:30-18:30) – 1.5 hrs

✓ Oct 17, Tues – Math (18:30-20:00) – 1.5 hrs

✓ Oct 18, Wed – Bio (18:30-19:30) – 1 hr

✓ Oct 19, Thurs – Math (17:30-18:30) – 1 hr

✓ Oct 24, Tues – Math (18:30-20:00) – 1.5 hrs

✓ Oct 25 , Wed – Bio (18:30-19:30) – 1 hr

~~☐ Oct 26, Thurs (Thea canceled due to fever)~~

~~☐ Oct 31, Tues – Halloween (week 44)~~

✓ Nov 01, Wed – Bio (18:30-19:30) – 1 hr

✓ Nov 02, Thurs – Math (17:30-18:30) – 1 hr

✓ Nov 07, Tues – Math (18:30-20:00) – 1.5 hrs

✓ Nov 08, Wed – Bio (18:30-19:30) – 1 hr

✓ Nov 09, Thurs – Math (17:30-18:30) – 1 hr

✓ Nov 14, Tues – Math (18:30-20:00) – 1.5 hrs

✓ Nov 15, Wed – Math (18:30-19:30) – 1 hr

✓ Nov 16, Thurs – Bio (17:30-18:30) – 1 hr

✓ Nov 19, Sun – Math (18:30-20:00) – 1.5 hrs

✓ Nov 21, Tues – Math (18:30-20:00) – 1.5 hrs

~~☐Nov 22, Wed Math (Thea canceled)~~

✓ Nov 23, Thurs – Bio (17:30-18:30) – 1 hr

✓ Nov 28, Tues – Math (18:30-20:00) – 1.5 hrs

✓ Nov 29, Wed – Bio (18:30-19:30) – 1 hr

✓ Nov 30, Thurs – Math (17:30-18:30) – 1 hr

✓ Dec 05, Tues – Math (18:30-20:00) – 1.5 hrs

~~☐ Dec 06, Wed – Bio (Rescheduled for Monday)~~

✓ Dec 07, Thurs – Math (17:30-18:30) – 1 hr

✓ Dec 10, Sun – Math (15:00-17:00) – 2 hrs

✓ Dec 11, Mon – Bio (19:00-20:00) – 1 hr

~~☐ Dec 12, Tues – (No Math after exam)~~

~~☐ Dec 13, Wed – (No Bio today)~~

~~☐ Dec 14, Thurs – (No Math after exam)~~✓ Dec 21, Thurs – Math (17:30-18:30) – 1 hr

☐ Dec 19, Tues – (No Math after exam)

☐ Dec 20, Wed – Bio (No Biology)

{ Holiday Break }

✓ Jan 10, Wed – Math (19:00-20:00) – 1 hr

✓ Jan 11, Thurs – Bio (18:00-19:00) – 1 hr

✓ Jan 15, Mon – Math (19:00-20:30) – 1.5 hrs

~~☐ Jan 17, Wed – Math (Thea cancelled) – 1 hr~~

~~☐ Jan 18, Thurs – Bio (Thea cancelled) – 1 hr~~

✓ Jan 22, Mon – Math (19:00-20:00) – 1 hr

✓ Jan 24, Wed – Math (19:00-20:00) – 1 hr

~~☐ Jan 25, Thurs – Bio (18:00-19:00) – 1 hr~~

✓ Jan 29, Mon – Math (19:00-20:30) – 1.5 hrs

✓ Jan 31, Wed – Math (19:00-20:00) – 1 hr

~~☐ Feb 01, Thurs – Bio (Thea canceled)~~

~~☐ Feb 05, Mon – Math (Thea canceled)~~

**Total Hours = 52 / 64**

⠀ Upcoming Lessons

To be Determined.